Question:
If \( A \) and \( B \) are invertible matrices, then which of the following is not correct?
If \( A \) and \( B \) are invertible matrices, then which of the following is not correct?
Show Hint
Matrix inverse operations follow specific rules. For addition, the inverse of a sum is not the sum of the inverses.
Updated On: Jun 16, 2025
- \( (A + B)^{-1} = B^{-1} + A^{-1} \)
- \( (AB)^{-1} = B^{-1} A^{-1} \)
- \( \text{adj} = |A| A^{-1} \)
- \( |A|^{-1} = |A^{-1}| \)
Hide Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
The formula \( (A + B)^{-1} = B^{-1} + A^{-1} \) is incorrect because matrix addition does not work the same way as matrix multiplication. The inverse of the sum of two matrices is not the sum of their inverses.
Was this answer helpful?
0
0
Top Questions on Matrices
- Let \( A = \begin{bmatrix} 2 & 0 \\ 0 & 3 \end{bmatrix} \). The determinant of \( A^3 \) is:
- Let \[ A = \begin{pmatrix} 1 & 4 \\ -2 & 1 \end{pmatrix} \quad \text{and} \quad C = \begin{pmatrix} 3 & 4 & 2 \\ 12 & 16 & 8 \\ -6 & -8 & -4 \end{pmatrix}. \] Then, find the matrix $B$ if $AB = C$.
- The matrix $A = \begin{pmatrix} \sqrt{3} & 0 & 0 \\ 0 & \sqrt{2} & 0 \\ 0 & 0 & \sqrt{5} \end{pmatrix}$ is a/an :
- If \[ \begin{bmatrix} 3 & -1 \\ 0 & 1 \\ 2 & -3 \end{bmatrix} A = \begin{bmatrix} 2 & -5 \\ -17 \end{bmatrix} \] then find matrix \( A \).
- If \[ \begin{bmatrix} 2x-1 & 3x \\ 0 & y^2-1 \end{bmatrix} = \begin{bmatrix} x+3 & 12 \\ 0 & 35 \end{bmatrix} \] then the value of \( (x - y) \) is :
View More Questions
Questions Asked in CBSE CLASS XII exam
In the given reaction sequence, the structure of Y would be:
- CBSE CLASS XII - 2025
- Aldehydes, Ketones and Carboxylic Acids
- A proton moving with velocity \( V \) in a non-uniform magnetic field traces a path as shown in the figure. The path followed by the proton is always in the plane of the paper. What is the direction of the magnetic field in the region near points P, Q, and R? What can you say about relative magnitude of magnetic fields at these points?
- CBSE CLASS XII - 2025
- Motion of charged particles in a magnetic field
- Explain why the milk produced by the mother during the initial days of lactation is considered to be very essential for the newborn infant.
- CBSE CLASS XII - 2025
- Applications of Biotechnology
- Table 1: Composition of India’s export : 2009-2017 (Percentage share in exports)
Commodities 2009-10 2010-11 2015-16 2016-17 Agriculture and allied products 10.0 9.9 12.6 12.3 Ore and minerals 4.9 4.0 1.6 1.9 Manufactured goods 67.4 68.0 72.9 73.6 Crude and petroleum products 16.2 16.8 11.9 11.7 Other commodities 1.5 1.2 1.1 0.5 - CBSE CLASS XII - 2025
- International Trade
- Hunting and Food Gathering
The earliest human beings depended on their immediate environment for their sustenance. They subsisted on: animals which they hunted; and the edible plants which they gathered from forests in the vicinity.
Primitive societies depended on wild animals. People located in very cold and extremely hot climates survived on hunting. The people in the coastal areas still catch fish though fishing has experienced modernization due to technological development. Many species, now have become extinct or endangered due to illegal hunting (poaching). The early hunters used primitive tools made of stones, twigs or arrows so the number of animals killed was limited. Gathering and hunting are the oldest economic activity known. These are carried out at different levels with different orientations.
Gathering is practised in regions with harsh climatic conditions. It often involves primitive societies, who extract, both plants and animals to satisfy their needs for food, shelter and clothing. This type of activity requires a small amount of capital investment and operates at very low level of technology. The yield per person is very low and little or no surplus is produced.- CBSE CLASS XII - 2025
- Gathering and Hunting
View More Questions